# Quick trigonometry question

1. Nov 12, 2008

### Inertialforce

1. The problem statement, all variables and given/known data
When dealing with periods and amplitudes in trigonometry, are all complete cycles (for cosine, sine, and tan functions) considered to be 360(degrees)?

I'm just wondering, because I want to make sure now so that I can apply it to the appropriate questions when the time comes.

2. Relevant equations

3. The attempt at a solution

2. Nov 13, 2008

### Дьявол

I think this is the right thing for you: http://catcode.com/trig/trig09.html

Also the period of the trigonometric functions is not same for all of them.

sin(x) and cos(x) have 2k$\pi$ period and tg(x) and ctg(x) have k$\pi$ period.

So if you have:
sinx=a:
$$x=\begin{bmatrix} arcsin(a)+2k\pi\\ \pi - arcsin(a)+2k\pi \end{bmatrix}$$
cosx=a:
$$x=\begin{bmatrix} \pm arccos(a)+2k\pi \\ \end{bmatrix}$$
tgx=a:
$$x=\begin{bmatrix} arctg(a) + k\pi \\ \end{bmatrix}$$
ctgx=a
$$x=\begin{bmatrix} arcctg(a) + k\pi \\ \end{bmatrix}$$

I hope this helped you.